# Maximum Lag Length allowed for DSGE-VAR Model with relatively high dimension and relatively medium sample length

Dear Johannes,
My current DSGE model has 9 observables, 9 structural shocks, the data is of quarterly frequency and the data length is 212 quarters. I have a question regarding the maximum lag allowed for a DSGE-VAR model, is any formula to relate between the maximum lag allowed, the number of observable variables and the sample length? Given the dimension of 9 observables, data length of 212 quarters. I understand that for determining the optimal lag length and the scaling factor (the relative sizes between artificial data and observable data) is to calculate and compare log marginal likelihoods from combinations of lag and scaling factor so as to choose the largest log marginal likelihood. However, I would like to know that given dimension of 9 observable variables and data length of 212 quarters, does the DSGE-VAR model only allow for lag 2? and are lags greater than 3 not possible?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

Think about estimating the VAR equation by equation with OLS. With 212 quarters, you can estimate at most 212 parameters. There will be a constant and with 9 series 9 parameters for each lag. With 3 lags, you will have 1+3*9= 28 parameters. That should be fine.

Dear Johannes,
Thank you very much, but I am still confused.
For 9 observable variables with 3 lags, in the case of the VAR equation by equation with OLS,
each equation there are 1 constant+3 lags for each of 9 observable variables, then for each equation, there should be 1+39=28 parameters, and there are 9 equations, so 289=252 parameters? and we also need to estimate covariance matrix of VAR coefficients, and the number of unknown coefficients for symmetric coefficient matrix is (99+9)/2=45, so in total number of unknow parameters for VAR (9) with 3 lags is (1+39)9+(99+9)/2=252+45=297, the number of observable data is (212-3)*9=209multiply9=1881, because 1881>297, the observable sample size is already sufficient right? and does this mean that adding any size of artificial data to observable data to estimate DSGE-VAR always have sufficient data size?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

1. You, if you are multiplying by the number of equations, you need to consider that you have 212 quarters times 9 variables.
2. Yes, estimating the covariance matrix will also require degrees of freedom.
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